Dot Product Calculator

About this calculator

This calculator computes the dot product of two 3D vectors, a·b = a₁b₁ + a₂b₂ + a₃b₃, a scalar (single-number) result that also equals |a||b|cos(θ), the product of the vectors' magnitudes and the cosine of the angle between them.

It's a core operation in physics for calculating work done by a force (W = F·d) and in 3D graphics and game development for lighting calculations and determining whether two vectors point in a similar direction (a positive dot product) or opposite directions (negative). Engineering and linear algebra students use it to check vector orthogonality — a dot product of exactly zero means the vectors are perpendicular.